Functional connectivity (FC) is a graph-like data structure commonly used by neuroscientists to study the dynamic behaviour of brain activity. However, these analyses rapidly become complex and time-consuming, since the number of connectivity components to be studied is quadratic with the number of electrodes. In this work, we address the problem of clustering FC into relevant ensembles of simultaneously activated components, yielding a multiplex network that reveals characteristic patterns of the epileptic seizures of a given patient. While $k-$means is certainly the most popular method for data clustering, it is known to perform poorly on large dimensional data sets, and to be highly sensitive to noise. To overcome the so-called curse of dimensionality, we propose a new tensor decomposition to reduce the size of the data set formed by FC time-series recorded for several seizures, prior to apply $k$-means. We propose an adapted procedure to infer a multiplex network from several FC time series, and we emphasise one particular variant that imposes sparsity constraint. Then, we conduct a real case study, applying the proposed sparse tensor decomposition to iEEG data to infer a multiplex network corresponding to the different stages of an epileptic seizure.
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